1D Generalised Burgers-Huxley: Proposed Solutions Revisited and Numerical Solution Using FTCS and NSFD Methods - Appadu, Appanah R.; Tijani, Yusuf O. (Frontiers in Applied Mathematics and Statistics, 2022)
In this paper, we obtain the numerical solution of a 1-D generalised Burgers-Huxley equation under specified initial and boundary conditions, considered in three different regimes. The methods are Forward Time Central Space (FTCS) and a non-standard finite difference scheme (NSFD). We showed the schemes satisfy the generic requirements of finite difference method in solving a particular problem. There are two proposed solutions for this problem and we show that one of the proposed solution contains a minor error. We present results using FTCS, NSFD and exact solution as well show how the profiles differ when the two proposed solutions are used. In this problem, the boundary conditions are obtained from the exact solution. Error analysis and convergence tests are performed.